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8
ANALYTICAL MECHANICS
C2 - az + 52 4. 2 ab cos 0
= (10 cm.)2 + (10 cm.)2 + 2 X10 cm. X 10 cm. coa (00°) = 300 cm.2 c = 10 \/3 cm. = 17.3 cm.* _    & sin 0 a + b cos 0
10 cm. sin (60°) 10 cm.+ 10 cm. cos (60°) -*V8. (9 = 30°.                                     0
X
Therefore the resultant displacement
is about 17.3 cm. along the direction N. 60° E.
Fiu. 8.
PROBLEMS.
1.   A vector which points East has a length of 10 nu., and another vector which points Southeast is 25 cm. long.   Find the direction and the magnitude of their sum.
2.   Find the direction and the magnitude of the diiTerence of the*, vectors of the last problem.
3.   The sum of two vectors is perpendicular to their difference.    Show that the vectors are equal in magnitude.
4.   The sum and the difference of two vectors have equal magnitudes. Show that the vectors are at right angles to each other,
13. Resolution  of Vectors   into  Compo- y nents.—The projection of a vector upon a line is called the component of the vector along that line.    The vectors aa and ay in Fig. 9, for instance, are the components of a along the x-axis and the y-axis, respectively. The following relations are evident from the figure and do not need further <> explanation.
Fio. !).
* The symbol " = " will be used to denote approximate equality. Therefore" = " should be read " equals approximately,JJ or "equal** about," or "equals nearly." See table of notations, p. x.